1. A 4 kg object moving to the left collides with and sticks to a 3 kg object moving to the right. Which of the following is true of the motion of the combined objects immediately after the collision?
(A) They must be moving to the left.
(B) They must be moving to the right.
(C) They must be at rest.
(D) The motion cannot be determined without knowing the speeds of the objects before the collision.
2. A brother and sister are standing next to each other at rest on a surface of frictionless ice. The brother’s mass is exactly twice that of his sister’s. The sister suddenly pushes her brother. As a result, the sister moves with kinetic energy K.What is the resulting kinetic energy of the brother?
(A) 4 K
(B) 2 K
3. At time t=0 , a cart is at x = 10 m and has a velocity of 3 m/s in the -x-direction . The cart has a constant acceleration in the +x-direction with magnitude 3 m/s2＜a＜6 m/s2 . Which of the following gives the possible range of the position of the cart at t=1s?
(A) 4 m＜x＜5.5m
(B) 8.5 m＜x＜10m
(C) 11.5 m＜x＜13m
4. The figure above shows part of a circuit containing three resistors and an ammeter. A steady current flows through the ammeter. Resistors R1 , R2 , and R3 have currents I1 , I2 , and I3,respectively. Which of the following expressions correctly relates the three currents?
(D) The relationship cannot be determined without information about the rest of the circuit.
The graph above shows the potential energy U of a system as one object in the system moves along the x-axis and the rest of the system does not move. Six evenly-spaced points along the x-axis are labeled. At point H, the object is moving in the positive x-direction and the mechanical energy of the system is 5.0 joules . As the object moves, no energy enters or leaves the system.
5. In which segment does the net force exerted on the object have the greatest magnitude?
1. (7 points, suggested time 13 minutes)
Two blocks, with masses m and 3m , are attached to the ends of a string with negligible mass that passes over a pulley, as shown above. The pulley has negligible mass and friction and is attached to the ceiling by a bracket. The blocks are simultaneously released from rest.
(a) Derive an equation for the speed v of the block of mass 3m after it falls a distance d in terms of m, d, and physical constants, as appropriate
(b) Determine the work done by the string on the two-block system as each block moves a distance d.
(c) The acceleration of the center of mass of the blocks-string-pulley system has magnitude aCOM. Briefly explain, in terms of any external forces acting on the system, why aCOM is less than g.